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  "body": "\n## Definition\n\nLet $a$ and $b$ be integers.\nThe integer $a$ divides $b$ when there is an integer $k$ such that $b = a k$.\nThe notation $a \\mid b$ means that $a$ divides $b$, and $a \\nmid b$ means that it does not.\nWhen $a \\mid b$, $a$ is a divisor (or a factor) of $b$, and that $b$ is a multiple of $a$.\n\n## Remarks\n\nEach integer divides $0$, because $0 = a \\cdot 0$. The integer $0$ divides only $0$.\nThe integers $1$ and $-1$ divide each integer.\nIf $a \\mid b$ and $b \\mid c$, then $a \\mid c$. On the natural numbers, divisibility is a partial order.\nIf $a \\mid b$ and $a \\mid c$, then $a \\mid (x b + y c)$ for all integers $x$ and $y$.\n\n## Explanations\n\n### L1 human\n\nThe integer $a$ divides $b$ when $b$ is in the list $\\dots, -2a, -a, 0, a, 2a, \\dots$ of the multiples of $a$.\nFor example, $3 \\mid 12$ because $12 = 3 \\cdot 4$.\nBut $5 \\nmid 12$, because no integer $k$ gives $5 k = 12$.\n",
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